The n candidates for a job have been ranked 1, 2, 3,..., n. Let X 5 the rank of a randomly selected candidate, so that X has pmf p(x)551yn x51,2,3,...,n 0 otherwise (this is called the discrete uniform distribution). Compute E(X) and V(X) using the shortcut formula. [Hint: The sum of the first n positive integers is n(n 1 1)y2, whereas the sum of their squares is n(n 1 1)(2n 1 1)y6.]

Question:

The n candidates for a job have been ranked 1, 2, 3,..., n.  Let x = rank of a randomly selected candidate, so that x has pmf:

(this is called the discrete uniform distribution).

Compute E(X) and V(X) using the shortcut formula.

[Hint: The sum of the first n positive integers is , whereas the sum of their squares is

or

Step-by-step explanation:

Given

PMF

Required

Determine the E(x) and Var(x)

E(x) is calculated as:

This gives:

From the hint given:

So:

Var(x) is calculated as:

Calculating:

Using the hint given:

So:

So:

Take LCM

Apply difference of two squares

the cat is blue because the probability of extension towards the prefix of the diameter of the circle could only mathematically equal to the sum of the roots of the carrots from   your garden.

step-by-step explanation: